We will get maximum volume at point x after checking with derivative test.
Maxima and minima of a function are the extreme within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.
We have a function f(x) that represents the volume of the box.
f(x) = x(13 - 2x)(15-2x)
The domain of the function will be all real numbers.
f(x) = (13x - 2x²)(15 - 2x)
f(x) = 195x-56x²+4x³
f'(x) = 195 - 112x + 12x² = 0
After calculating and checking f''(x)
We will get maximum volume at:
[tex]\rm x = \dfrac{28-\sqrt{199}}{6}[/tex]
And the maximum volume:
[tex]\rm Volume_{max}= \dfrac{2618+199\sqrt{199}}{27}[/tex]
Thus, we will get maximum volume at point x after checking with derivative test.
Learn more about the maxima and minima here:
brainly.com/question/6422517
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